How long have canvas mouse events been broken?

Nope - I only get one EVENT_MOUSEMOVE if I move to a pixel. Regarding the jumping, this tweak (incoroporated below) should fix it:

' createcanvas.bmx

Framework brl.win32maxgui
Import brl.eventqueue
Import brl.d3d7max2d
'Import brl.glmax2d

Strict 

Global GAME_WIDTH=720
Global GAME_HEIGHT=480

' create a centered window with client size GAME_WIDTH,GAME_HEIGHT

Local wx=(ClientWidth(Desktop())-GAME_WIDTH)/2
Local wy=(ClientHeight(Desktop())-GAME_HEIGHT)/2

Local window:TGadget=CreateWindow("My Canvas",wx,wy,GAME_WIDTH,GAME_HEIGHT,Null,WINDOW_TITLEBAR|WINDOW_CLIENTCOORDS)

' create a canvas for our game

Local canvas:TGadget=CreateCanvas(0,0,320,240,window)
Local canvas1:TGadget'=CreateCanvas(340,140,320,240,window)

' create an update timer
Local picked:TGadget
Local handlex,handley

'CreateTimer 60

While WaitEvent()
	Local src:TGadget=TGadget(EventSource())
	DebugLog CurrentEvent.toString()
	Select EventID()
		Case EVENT_TIMERTICK
			RedrawGadget canvas

		Case EVENT_GADGETPAINT
			SetGraphics CanvasGraphics(src)
			SetOrigin 160,120
			SetLineWidth 5
			Cls
			Local t=MilliSecs()
			DrawLine 0,0,120*Cos(t),120*Sin(t)
			DrawLine 0,0,80*Cos(t/60),80*Sin(t/60)
			Flip
			
		Case EVENT_MOUSEDOWN
			picked=src
			handlex=EventX()+GadgetX(src)
			handley=EventY()+GadgetY(src)

		Case EVENT_MOUSEUP
			picked=Null

		Case EVENT_MOUSEMOVE
			If picked
				Local mx=EventX()+GadgetX(src)-handlex
				Local my=EventY()+GadgetY(src)-handley
				SetGadgetShape(src,mx,my,GadgetWidth(picked),GadgetHeight(picked))
			EndIf
	
		Case EVENT_WINDOWCLOSE
			FreeGadget canvas
			End

		Case EVENT_APPTERMINATE
			End
	End Select
Wend